Construction of Haar Measure on Projective Limit Group and Random Order Values of Non-atomic Games 1
نویسندگان
چکیده
By superimposing a group structure on a sequence of projective probability spaces of Lebesgue measure preserving (l.m.p.) automorphisms of unit interval, the paper extends the Daniel-Kolmogorov consistency theorem that enables the construction of a measurable group structure with invariant Haar probability measure on an uncountably large projective limit space. The projective limit group is then represented as a subgroup of the group of l.m.p. automorphisms and constitutes a group of random orders. With respect to this group of random orders, and using the generalized consistency theorem again, a formula for the unique random order value operator, proposed in Raut [1993], is derived for a class of scalar and vector measure valued games in pNA and the formula is seen to be identical with the axiomatic value formula of such games in Aumann and Shapley [1974]. Construction of Haar measure on projective limit group and random order values of non-atomic games
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